If you had three to four months off a year to sail, would you base your boat out of the eastern Caribbean or Florida/Bahamas? Costs for storage for eight months a year, the cost of living in both areas, cruiser friendly areas, wind, anchorages, air fares, etc. Where would you want to be? Say the boat is around a to 30' inexpensive older but well set up sailboat and living aboard.

Keeping the boat in the Eastern Caribbean would be substantially more expensive and risky than in Florida. You would be flying in and out in high season with extraordinary air fares. You would be competing with all of the charter boats (most with barely competent skippers) for anchorages, mooring balls, and stools at the bar. When laid up for the hurricane season it is far more likely that you will experience the boat being hit by a hurricane than in Florida.

That said Florida can get quite cold in January/February.

My advice:
Option 1: Base in Florida, sail the southern part of the Bahamas and the Turks.
Option 2: (I agree preferred): Move the boat every year so that you get to experience different places.

When I've had a similar choice, I kept it in the U.S. and took it over to the Bahamas. (kept it there on the hard one year).

I think the Bahamas have much to offer and are very accessible to the U.S. I personally like being able to easily bring it back to the U.S. if needed where I have easy access to marine stores, all my tools, my car, etc, to do work on it.

I also just like the diversity of the Bahamas. In addition to the marinas, and small towns, one can spend a week or more enjoying unihabied islands with anchorages to yourself.

I also own a boat, in the BVIs, but it's taken care of by a charter company. It's personally, not where I choose to keep a boat as an absentee owner, if I was responsible for it myself. In addition to greater distance, I found long-term storage options to be chaper in the Bahamas.

Of course, much of it comes down to your personal desires and what locations appeal to you most.

Keep it in Florida and cruise the Bahamas. Or, you can even do the southwestern Caribbean on that schedule with a little bit of planning. To me leaving a boat in the eastern Caribbean would be too problematic: long way away so you might need to spend a lot of time getting the boat going again each year, more hurricane prone and fewer safe places to leave it, flights are much more expensive and limited, paperwork and hassles, etc. However, all that being said, you might want to just move it around as you see fit, though it would be hard to find a reasonable place to leave it in the Eastern Caribbean in December, which is the beginning of the height of the season.